Large amplification in stage-structured models: Arnol’d tongues revisited
Large amplification in stage-structured models: Arnol’d tongues revisited
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阶段结构模型中的大放大：重新审视阿诺尔的舌头
DOI：
10.1007/s00285-004-0264-8
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发表时间：
2004
影响因子：
1.9
通讯作者：
T. G. Benton
中科院分区：
文献类型：
--
作者：
J. V. Greenman;T. G. Benton
一系列的阶段结构的离散时间模型的周期和点吸引子的共存已被证实。周期性的吸引子循环具有很大的振幅，当与平衡水平相比时，种群在极低和令人惊讶的高值之间循环。在这种情况下，一个稳定的状态可能会被足够强度的噪声冲击到一个高波动性的状态。我们发现，这些大振幅周期的来源是Arnol的舌头，参数空间的特殊区域，系统表现出周期性的行为。这些舌状物中的大多数完全位于系统不稳定的参数空间中，但也有例外，这些例外是导致吸引子共存的舌状物。在所考虑的模型范围内，阿诺舌头的几何形状相似，这可能表明这是舞台结构模型的一个共同特征，但在缺乏证据的情况下，这只能是一个有用的工作假设。分析表明，虽然大幅度周期可能存在数学上，他们可能无法访问生物学，如果生物的限制，如人口密度和生命率的非负性，施加。无障碍被发现是高度敏感的模型结构，即使数学结构不是。这凸显了从特定模型中得出生物学结论的危险。有一个全面的观点，周期性状态可以出现在离散时间模型的家庭的不同机制是重要的辩论周期性的原因，在特定的生态系统是内在的，环境或营养。本文是对这一持续辩论的贡献。
The coexistence of periodic and point attractors has been confirmed for a range of stage-structured discrete time models. The periodic attractor cycles have large amplitude, with the populations cycling between extremely low and surprisingly high values when compared to the equilibrium level. In this situation a stable state can be shocked by noise of sufficient strength into a state of high volatility. We found that the source of these large amplitude cycles are Arnol’d tongues, special regions of parameter space where the system exhibits periodic behaviour. Most of these tongues lie entirely in that part of parameter space where the system is unstable, but there are exceptions and these exceptions are the tongues that lead to attractor coexistence. Similarity in the geometry of Arnol’d tongues over the range of models considered might suggest that this is a common feature of stage-structured models but in the absence of proof this can only be a useful working hypothesis. The analysis shows that although large amplitude cycles might exist mathematically they might not be accessible biologically if biological constraints, such as non-negativity of population densities and vital rates, are imposed. Accessibility is found to be highly sensitive to model structure even though the mathematical structure is not. This highlights the danger of drawing biological conclusions from particular models. Having a comprehensive view of the different mechanisms by which periodic states can arise in families of discrete time models is important in the debate on whether the causes of periodicity in particular ecological systems are intrinsic, environmental or trophic. This paper is a contribution to that continuing debate.